Before I continue, for my non-Catholic friends, it may be difficult to understand what Catholics believe about Mary. There's not enough room in this post to try to explain in detail, but I do want to mention only a few things.
We do not worship Mary. Worship, also referred to as adoration is attributed only to God. However, as the Mother of God (as Jesus is true man, true God), we have a special devotion to Mary and honor her. This devotion in no way takes away from the worship and adoration given to God. In fact, as Mary completely subjected her will to the Will of God, her life always points and directs us to a more intimate relationship with Jesus.
The Church rightly honors the Blessed Virgin with special devotion. From the most ancient times the Blessed Virgin has been honored with the title of 'Mother of God,'...This very special devotion differs essentially from the adoration which is given to the incarnate Word and equally to the Father and the Holy Spirit, and greatly fosters this adoration. - from Catechism 971Just contemplate what "maternity of Mary" indicates. Jesus, our Almighty God, humbled Himself, taking on flesh (Mary's flesh) and became man. Wait! He became a baby. Yes, a baby!
For 40 weeks, He lived in Mary's womb!. In the Old Testament, the Ark of the Covenant carried the tablets of the Law, the rod of Aaron signifying the sacerdotal of the priesthood, and manna. What is the Ark, if not a prefiguring of the new Ark of the New Covenant? For did not Jesus live in Mary? Did Mary not contain within her very body the Author of the Law, the true High Priest, and the Bread come down from Heaven, the flesh given for the life of the world?
O Jesus, living in Mary, come and live in your servants, in the spirit of holiness, in the fullness of your power, in the perfection of your ways, in the truth of your virtues, in the communion of your mysteries. Rule over every adverse power, in your Spirit, for the glory of the Father. Amen. - 17th century prayer